1. Radoslav Forgáč, Igor Mokriš
Institute of Informatics
Slovak Academy of Sciences
Bratislava, Slovakia
Pulse Coupled Neural Network Models for Dimension Reduction of Classification Space
Radoslav Forgáč, Igor Mokriš
WIKT 2006, – , Bratislava

2. Outline Goal of our research
Why we use Pulse Coupled Neural Network (PCNN)?
Introduction to PCNN
Structure of PCNN neuron
Mathematical model of PCNN neuron
Feature generation by PCNN
Purposes of PCNN modification
Overview of PCNN modifications
OM-PCNN versus ICM neuron

3. Goal of our research Dimension reduction of classification space
Dimension space of input image D
Input image D
Dimension reduction of classification space
Minimization of the number of iteration steps by O-PCNN
Feature generation
n; n << D
Dimension reduction of feature space
d << D
Feature selection
d; d < n
Dimension of classification space d
Classification d
Class 1
Class 2
Class X

4. Why we use PCNN? PCNN Properties
Invariant to geometrical transformations
Fixed structure of neural network
Learning – free
Minimal set of image etalons, i.e. only one etalon for every class
Properties of Standard Neural Networks
Generated features are not invariant to geometrical transformations
Problem to set the optimal structure of NN and its parameters
High time consumption especially by gradient methods of learning
Typical learning problems – overlearning, looking for local minimum of error function

5. Introduction to PCNN One-layer, two dimension NN
Lateral connection of weights
The PCNN structure is the same as the structure of the input object matrix S

6. Structure of PCNN neuron
Primary and Linking input
Linking part
Pulse generator

7. VL, VF,, Vq :coefficients of potentials
Mathematical model of PCNN neuron
Input part
image pixel intensity
iteration step
W1, W2: weight matrix
Feeding input:
Linking input
Linking part
aL , aF : decay coefficients
VL, VF,, Vq :coefficients of potentials
Internal activity of neuron:
Pulse generator
activated neuron
linking coefficient
Output:
non-activated neuron
Threshold potential:

8. Feature generation by PCNN
input image
PCNN output in
3. iteration step
generated feature
in 28. iteration step
PCNN output
vector of generated features

9. Purposes of PCNN modification
reduction the number of generated features
and high recognition precision preservation
reduction of PCNN parameters
optimization of PCNN parameters
determination of optimal number of iteration steps N
selection of features with the highest information value
increasing the invariance of generated features against rotation, dilation and translation of images

10. Overview of PCNN modifications
PCNN with modified primary input (M-PCNN)
Fast linking PCNN
Feedback PCNN
PCNN with Linear Decay Threshold
Intersecting Cortical Model - ICM
Optimized M-PCNN (OM-PCNN)

11. OM-PCNN vs. ICM neuron
OM-PCNN neuron
ICM neuron

12. Thank you for your attention